stevecartwright - the option series that end in 00 or 50 (e.g. 4400, 4450, 4500 etc) are American style options, and can be assigned at anytime. This means that in the case of the 4400 puts, if the index spiked down, the buyer of the options you have sold could exercise them and demand that you deliver at 4400, which could be painful if the index has spiked down to 4300. Even more galling then if the market moves back up again above 4400 by expiry.
The series that end in 25 and 75 (4425, 4475, 4525 etc) are European style, and these can only be exercised at expiry. This means that if the index spikes down, the holder of the option can sell in the market, but cannot exercise them against the holder until expiry. In practice there is just a cash settlement for the difference between the strike price and the actual price if the options are still ITM. So if you are short but expect the position to pull back your way, you can hold on without having to worry about whether you are going to get assigned, and then get the expected move taking place after you have been "ejected" from the party.
HTH